How can there be inflation at different rates within the same currency zone? For example, how can there be higher inflation in Greece than in Germany, despite having the same currency?
Effectively, you are asking: how can there be different prices across countries within the same currency zone? This may sound surprising because within the Euro common currency, for example, we label regions as countries and there is a price index computed for each country. While, for example, the US -- which is itself a well-established currency union -- there is typically one such computed price. However, if we were to impute different prices for each US state (here you can think of different states as different countries within a common US currency zone), then we would also get very different numbers! This is why, even within the US, we talk about the cost of living being different depending on where you live. And the cost of living can change at different rates (i.e., regions can have different inflation rates) depending on the particular supply and demand conditions across regions.